In an early article describing how people learn, the rate of change of the probability that a person performs a task correctly (p) with respect to time (t) is given by

where k and m are constants related to the rate that the person learns the task. For this exercise, let m = 4 and k = 0.5.

(a) Letting p = 0.1 when t = 0, use Method 2 or 3 in Example 1 to construct a table for t_i and p_i like the ones in the examples for 0 ≤ x ≤ 30, with h = 5.
(b) Based on your answer to part (a), what does p seem to approach as t increases? Explain why this answer makes sense.

`zle (zd - d)= m 2k = dt dp